This notebook was prepared by Donne Martin. Source and license info is on GitHub.

Solution Notebook

Problem: Determine if a string s1 is a rotation of another string s2, by calling (only once) a function is_substring.


  • Can we assume the string is ASCII?
    • Yes
    • Note: Unicode strings could require special handling depending on your language
  • Is this case sensitive?
    • Yes
  • Can we use additional data structures?
    • Yes
  • Can we assume this fits in memory?
    • Yes

Test Cases

  • Any strings that differ in size -> False
  • None, 'foo' -> False (any None results in False)
  • ' ', 'foo' -> False
  • ' ', ' ' -> True
  • 'foobarbaz', 'barbazfoo' -> True


Examine the following test case:

  • s1 = 'barbazfoo'
  • s2 = 'foobarbaz'

We see that if we can use the given is_substring method if we take compare s2 with s1 + s1:

  • s2 = 'foobarbaz'
  • s3 = 'barbazfoobarbazfoo'


  • Time: O(n)
  • Space: O(n)


In [1]:
class Rotation(object):

    def is_substring(self, s1, s2):
        return s1 in s2

    def is_rotation(self, s1, s2):
        if s1 is None or s2 is None:
            return False
        if len(s1) != len(s2):
            return False
        return self.is_substring(s1, s2 + s2)

Unit Test

In [2]:
import unittest

class TestRotation(unittest.TestCase):

    def test_rotation(self):
        rotation = Rotation()
        self.assertEqual(rotation.is_rotation('o', 'oo'), False)
        self.assertEqual(rotation.is_rotation(None, 'foo'), False)
        self.assertEqual(rotation.is_rotation('', 'foo'), False)
        self.assertEqual(rotation.is_rotation('', ''), True)
        self.assertEqual(rotation.is_rotation('foobarbaz', 'barbazfoo'), True)
        print('Success: test_rotation')

def main():
    test = TestRotation()

if __name__ == '__main__':
In [3]:
%run -i
Success: test_rotation